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Elliptic–Hyperbolic Partial Differential Equations

A Mini-Course in Geometric and Quasilinear Methods

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Éditeur :

Springer


Collection :

SpringerBriefs in Mathematics

Paru le : 2015-07-08



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Description

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example:
 
• The heating of fusion plasmas by electromagnetic waves
• The behaviour of light near a caustic
• Extremal surfaces in the space of special relativity
• The formation of rapids; transonic and multiphase fluid flow
• The dynamics of certain models for elastic structures
• The shape of industrial surfaces such as windshields and airfoils
• Pathologies of traffic flow
• Harmonic fields in extended projective space
 
They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications.
 
Elliptic-Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.
Pages
128 pages
Collection
SpringerBriefs in Mathematics
Parution
2015-07-08
Marque
Springer
EAN papier
9783319197609
EAN PDF
9783319197616
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
12
Taille du fichier
2202 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
52,74 €
EAN EPUB
9783319197616
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
12
Taille du fichier
1536 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
52,74 €

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